The relevance of the work lies in the development of methods for structurally solving the problem of ensuring the astatic properties of discontinuous control systems in the conditions of improving electromechanical systems. The elemental base of modern electric drives maximizes the mass implementation of discontinuous control systems, which have a unique combination of operational properties. But the advantages resulting from this combination find practical implementation only with correct theoretical justification. The purpose of the study is to synthesize optimal control algorithms and means for calculating flexible feedback for a relay control system for an electric drive. Modification of differential slip equations allows for the structural synthesis of relay systems with the desired astatic properties. Implementation of astatic control algorithms requires the use of derivative observers, the effectiveness of which requires confirmation by modeling dynamics, which is also the goal of the work. To achieve these goals, a mathematical model was built, optimal parameters were calculated, a structural synthesis of various system options was carried out, and their transient processes were studied. The mutual independence of the sliding modes of electric drive regulators and differentiators made it possible to decompose the problem of synthesizing an integral control system into three simpler subtasks, which is fundamentally impossible in the case of continuous systems. The result of the work is the structure and parameters of an astatic electric drive control system, the properties of which are verified by numerical experiment. The use of derivative observers with relay control algorithms makes it possible to effectively implement structural solutions suitable for the implementation of astatic control systems for electric drives. The result of the work is also a procedure for applying the mathematical apparatus of the N–i switching method for the synthesis of observers, which are second-order systems. A promising direction for continuing this research is the integration of this procedure into algorithms for setting up relay optimal control systems.

Актуальність роботи полягає в розвитку методів структурного розв'язання задачі забезпечення астатичних властивостей систем розривного керування в умовах вдосконалення елементної бази електроприводів. Метою дослідження є синтез алгоритмів оптимального керування та засобів обчислення гнучких зворотних зв'язків для релейної системи керування електроприводом. Для досягнення цієї мети в роботі побудовано математичну модель, виконано розрахунок параметрів, здійснено структурний синтез різних варіантів системи та дослідження їх перехідних процесів. Результатом роботи є структура та параметри астатичної система керування електроприводом, властивості якої перевірено чисельним експериментом.